REACTOR SOURCE MODELS

3.1.1 Introduction

MCNP-compatible sources were prepared that represent neutron and photon radiation from a typical PWR core. Source descriptions were prepared that represent conditions while the reactor is at power and also at various times following shutdown. Neutrons and photons that result directly from the fission process (when the reactor is at power) are referred to as “prompt.” Decay neutrons and decay photons were also considered. These arise from decay processes in the spent fuel following shutdown. Decay neutrons consist of spontaneous-fission neutrons together with neutrons that arise as a result of (α,n) reactions on oxygen nuclei. By far, the majority of decay neutrons result from spontaneous fission of

242Cm and²⁴⁴Cm. Decay photon radiation results from photon decays following beta decay of the many neutron- rich fission products in the spent fuel.

When considering prompt neutron radiation, it is conventional to consider the associated delayed component also. However, the delayed component was not considered as a separate entity. Its intensity is less than 1% of that of the prompt and, given that reactor shutdown is not instantaneous, it was assumed that the reactor was at full power until completely shut down. This assumption ensured a conservative approach. In the case of the photon radiation, the first minute or so following shutdown proves difficult to characterize. During this time, the photon intensity is dropping rapidly and cannot be well

characterized by either the fission photon spectrum or by the photon decay libraries for spent fuel. Our approach, therefore, was to assume the reactor is at power until such time that the radiation source can be accurately described by the decay photon radiation.

The source characterizations developed in this work refer to a PWR operating at a power level of 1650 MW(t). The total core inventory is 46.1 tHM (tonnes of heavy metal, meaning uranium in this case), and the average maximum burnup is 39 GWd/MT. Therefore, the prompt neutron and photon sources apply to a fission rate that corresponds to 1650 MW. For the decay sources, a number of scenarios have been assumed, and in developing the decay sources, it was assumed they would apply to the full-core conditions at midcycle. We assumed there are three separate core loadings present at any time: one-third of the core is in its first cycle, one-third has been irradiated for one cycle and is in its second cycle, and one-third of the core has been irradiated for two cycles and is in its third cycle.

3.1.2 Spatial Arrangement of Source in the PWR Core

The radiation source is contained in the actinide and fission-product species that are present in the fuel rods. By defining the energy spectra for the neutrons and photons in terms of what is known for fuel in an operating reactor, or for spent fuel as the case may be, and with the surrounding core material properly defined, one obtains a true rendition of the resulting energy spectra outside the core. One possible source definition would be to specify the fuel rods in terms of diameters, lengths, and spacing. Such an

arrangement is practical for the case of an individual assembly but is overly cumbersome when an entire reactor core is to be defined. For the core as a whole, it is practical to homogenize the core material and to distribute the source material throughout the core, with the possible addition of zones to allow for radial patterns. In this particular work, however, because of the requirements of a number of codes that were being executed, it was found to be convenient to place a lattice of source points throughout the core.

The lattice consisted of horizontal arrays of source points at evenly spaced axial positions. Twenty-five axial positions were chosen with a horizontal array of 164 source points at each one, for a total of 4100 source points within the PWR core.

The source-strength distribution within the core is not uniform: it has axial and radial variations.

Figure 20 shows a typical axial profile for the power level for a PWR. This axial profile was employed when defining the source strengths. The profile in Fig. 20 is from a Swedish PWR for which detailed burnup information was available to us in numerical format (SKB, 2003) and is representative of a typical PWR. The profile was fit analytically (sixth-order polynomial using only even-parity terms) and was used in the code that produces the source-definition description.

To account for radial source variations, it was assumed that the source intensity in roughly the outer one-assembly thickness in the radial direction was reduced to 50% of the central intensity and the intensity in the next inward one-assembly thickness was reduced to about 75% of the central assembly intensity.

Figure 21 shows the resulting radial pattern based on these assumptions (for the array of horizontal points). The active core radius is 122.5 cm. Note that this is an effective value because of the irregular nature of the outer edge of the core.

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Fig. 20. Axial power profile (proportional to relative burnup) assumed for source definition.

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Fig. 21. Radial pattern of source strengths used for the PWR source definition.

determined from the concentrations for spontaneous-fission species, supplemented by the neutron contributions resulting from the alpha decays that cause (,n) reactions on oxygen isotopes.

3.1.4 Prompt Neutron Spectra

Neutrons from the fission process can be characterized by a Maxwellian distribution. However, for shielding purposes, where high-energy neutrons are of importance, a somewhat better representation is obtained using what is generally known as the Watt spectrum (Watt, 1952). A number of researchers seem to have proposed this shape, which was probably first reported in the literature by Watt, when he documented his measurements on fission-neutron spectra. Cranberg et al. (1956), who reported on extended measurements some years later, also discuss this representation of the neutron spectrum. The Watt spectrum can be described by

( )E 0.453exp( 1.036 ) sinh(2.29 )E E1/ 2

   , (1)

which gives the probability (per MeV) that a neutron is emitted with energy E (MeV). We assume 202.2 MeV/fission (²³⁵U) and 2.5 neutrons per fission. This yields 7.728 × 10¹⁶neutrons ∙ s^-1∙ MW^-1. Thus, using the value of E, the effective bin energy, the reactor power in megawatts, and the bin width in MeV, one can use ( )E to calculate the number of neutrons per second in the bin. A fission neutron spectrum, calculated using the Watt formula, is shown in Fig. 22. This spectrum was determined using the 22-group neutron energy structure and represents neutron totals from a PWR operating at 1650 MW.

The Watt spectrum is considered to give a good rendition of the fission neutron energy spectrum.

However, it was developed when investigating²³⁵U fission. Thus, the values of the numerical constants will be slightly dependent on the fissioning nuclide. Updated values for the constants have been proposed from time to time. [For an extensive discussion, see Madland and Nix (1982)]. For the purposes of the shielding calculations for which this work is intended, the values used here are considered to be

sufficiently accurate. However, two issues need to be mentioned with regard to the accuracy of the calculation of the neutron fission spectrum: firstly, the simple assumption that the bin energy, Eb, was chosen to be the energy at the bin center and, secondly, that the normalization was done by matching the total neutron count between lowest and highest bin edges to the theoretical total, which applies from zero to infinity. These issues are probably of negligible importance here. However, they can easily be addressed and future calculations will be adjusted accordingly.

2 10¹⁹ 3 10¹⁹ 4 10¹⁹ 5 10¹⁹

neutrons/MeV/seutrons∙MeV-1∙s-1

3.1.5 Decay Neutron Spectra

Decay neutrons result from spontaneous fission and (,n) reactions on¹⁷O and¹⁸O as a result of alpha decay of actinides. Rinard et al. (1981) show examples of calculations that determine such decay neutron spectra for spent PWR fuel. They use a Maxwellian distribution to represent the spontaneous fission neutrons. For the (,n) neutrons, they use empirical fits to a neutron spectrum resulting from²³⁸Pu alpha decay and conclude that this is also appropriate for the other alpha-decay processes of interest. The Maxwellian distribution gives the normalized neutron intensity as

/

Rinard et al. report that a spectral temperature, T, of 1.2 MeV is appropriate for uranium and plutonium nuclides and that 1.5 MeV is appropriate for²⁴²Cm and²⁴⁴Cm. In developing the spectra that are of interest here, spontaneous fission of²⁴²Cm and²⁴⁴Cm was responsible for about 40 and 50%, respectively, of the decay neutrons. Most of the remainder was from neutrons that result from (,n) reactions

involving²³⁸Pu decay alphas. As indicated for the prompt fission neutrons, the Watt spectrum gives a better representation of the high-energy neutrons than does a Maxwellian. This may also be true for the spontaneous-fission neutrons, and the matter will be considered in future work.

As regards the (,n) component, the neutron spectrum arising from²³⁸Pu alpha decay was parameterized by Rinard et al. as follows:

( ) _tot ( )

N E N F E , 

where the function F(E) is composed of three segments.

( ) 0.2207 6.4

Decay neutron spectra are shown in Fig. 23. Spontaneous-fission and (,n) neutrons are separately identified. These particular spectra refer to the case of one MT of discharged fuel following burnup to 39 GWd. Both the different shapes and the relative importance of the spontaneous-fission and the (,n) components can clearly be seen.

1 10⁸

3.1.6 Determination of Photon Spectra

The photon spectrum associated with the prompt photons was calculated using an empirical fit. The decay photon spectrum was calculated using an ORIGEN-S decay case following a TRITON simulation of burnup in a PWR. [ORIGEN-S and TRITON are components of the ORNL SCALE (SCALE, 2006) code system.]

Chilton et al. (1984) discuss the energy spectrum of prompt photons that result from the fission process.

They give an empirical fit of the form

( ) 6.7 exp( 1.05 ) 30exp( 3.8 )

N E   E   E , (4)

where N(E) gives the number of photons per MeV per fission. This empirical fit applies to the range 0.3 to 7 MeV. Prompt photon spectra calculated here were determined using this fit. The value at 0.3 MeV was extended to values of N(E) below 0.3 MeV, and for all values of E above 7 MeV, N(E) was assigned the 7-MeV value. For our purposes here, photons below 0.3 MeV are probably not of great importance;

however, by extending the 7-MeV value upward, we introduce a level of conservatism because we overestimate the flux at higher energies.

An example of a fission photon spectrum calculated with the above formula is shown in Fig. 24. The extension of the 0.3- and 7-MeV values can be seen. This calculation refers to a fission rate of 35.8 MW (about one assembly). According to Chilton et al. (1984), the lower part of the spectrum should yield about 10.5 photons ∙ MeV^-1∙ fission^-1. The values in this region for Fig. 24 are consistent with this value for the power level used in the calculations.

Decay photon spectra were obtained from ORIGEN-S decay cases. For these purposes the TRITON code was executed to simulate the full course of fuel burnup. Then, from the intermediate burnup steps, the ORIGEN-S decay calculations estimated the photon spectra associated with the fuel mixtures for

midcycle conditions. Examples of photon decay spectra are shown in Fig. 25. However, these spectra are not for a midcycle mix of fuel. Rather, they are for the case of 1 MT of fuel irradiated to 39 GWd.

Nevertheless, they are representative of the types of photon spectra that apply in these kinds of calculations. Spectra are shown at cooling times of 1 day, 1 week, and 1 month.

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3.1.7 Details of Source-Preparation Procedures

The determination of prompt neutron and prompt photon spectra was carried out using the fission-neutron and fission-photon spectral descriptions outlined above. For the required group structure, neutron

intensities were calculated for the group midpoints, and counts were then assigned to the groups based on the group width.

All decay sources were determined by running a TRITON case for a total burnup of 39 GWd/MT and then using ORIGEN-S with the intermediate TRITON output data at 6.5, 19.5, and 32.5 GWd/MT to produce decay output data for 1 day, 1 week, and 1 month. During the determination of the decay neutron sources, concentrations were obtained for the important spontaneous-fission and (α,n) species. These concentrations were then used to calculate decay neutron spectra [using the technique of Rinard et al.

(1980)] for the three values of assembly burnup at each of the decay times. Neutron intensities were calculated for the group midpoints, and group count rates were then determined based on the group width.

For each of the three decay times, the 6.5-, 19.5-, and 32.5-GWd/MT neutron spectra were used to produce a core-average spectrum.

The photon source spectra were obtained directly from ORIGEN-S, and for each decay time a core-averaged source spectrum was again calculated by averaging over the data for the three values of burnup.

When one runs ORIGEN-S, one gives the group structure as part of the input and ORIGEN-S determines photon count rates for the groups. It should be mentioned that neutron spectra can also be obtained directly from ORIGEN-S as an alternative to using the approach of Rinard outlined above. A quick comparison of some of the ORIGEN-S output neutron spectra showed good agreement with the corresponding spectra that were calculated as outlined above. The Rinard approach was used here because it was easy to implement. However, future work may use ORIGEN-S in developing the neutron spectra. In our work so far, it is not clear that the two approaches are noticeably different.

We have used averages of decay spectra from fuel irradiated to 6.5, 19.5, and 32.5 GWd/MT to be representative of the history of the fuel in the PWR core. However, it is not likely that fuel with different irradiation histories would be randomly distributed in the reactor core. It might be more realistic to define separate sources for groups of assemblies with different irradiation histories and to locate these sources more realistically in the core (e.g., in different radial zones). Although this would be likely to provide a more accurate rendition of the reactor’s effective source characteristics, it is not clear that it would have a noticeable impact on the intended transport calculations. If time permits, this issue will be addressed at a future date.